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3 years ago

What is the probability that the value the standard normal random variable assumes will be greater than 0.64?

1 answer:

5 0

For the answer to the question above, I'll provide a computation on my answer to give clarity and understanding to my answer.
P(z> 0.64) = 1- P(z<0.64) 
P(z<0.64) = .73891 
P(z> 0.64) = 1- 0.73891 =
So the answer to your question is
0.26109

I hope my answer helped you. Have a nice day!

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The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after

Olenka [21]

To solve this we are going to use the half life equation $N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) }$
Where:
$N_{0}$ is the initial sample
$t$ is the time in years
$t_{1/2}$ is the half life of the substance
$N(t)$ is the remainder quantity after $t$ years

From the problem we know that:
$N_{0} =100$
$t=200$
$t_{1/2} =1600$

Lets replace those values in our equation to find $N(t)$ :
$N(200) =100e^{( \frac{(-0.693)(200)}{1600}) }$
$N(200)=100e^{( \frac{-138.6}{1600} )}$
$N(200)=100e^{-0.086625}$
$N(200)=91.7$

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

8 0

2 years ago

Could someone help me, please?

k0ka [10]

We can rewrite the expression under the radical as

$\dfrac{81}{16}a^8b^{12}c^{16}=\left(\dfrac32a^2b^3c^4\right)^4$

then taking the fourth root, we get

$\sqrt[4]{\left(\dfrac32a^2b^3c^4\right)^4}=\left|\dfrac32a^2b^3c^4\right|$

Why the absolute value? It's for the same reason that

$\sqrt{x^2}=|x|$

since both $(-x)^2$ and $x^2$ return the same number $x^2$ , and $|x|$ captures both possibilities. From here, we have

The absolute values disappear on all but the $b$ term because all of $\dfrac32$ , $a^2$ and $c^4$ are positive, while $b^3$ could potentially be negative. So we end up with

$\dfrac32a^2\left|b^3\right|c^4=\dfrac32a^2|b|^3c^4$

3 0

3 years ago

A punch recipe calls for mixing 7 parts of cranberry juice with 4 parts of lemon juice. Find how much cranberry juice should be

Butoxors [25]

Answer:

Proportion- 1 to 21 or 1:21

Cranberry Juice- 147 ounces

Step-by-step explanation:

84/4 = 21

7*21 = 147

3 0

2 years ago

Sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 meters cubed.

Mrrafil [7]

Answer:

C. 128/3 meters cubed

Step-by-step explanation:

The volume of a cylinder is denoted by: $V=\pi r^2h$ , where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:

$V=\pi r^2h$

$64=\pi r^2h$

We know that the sphere and cylinder have the same height and radius. However, the "height" of a sphere is actually the same as its diameter, which is twice its radius. Then, we can replace h in the above equation with 2r:

$64=\pi r^2h$

$64=\pi r^2*2r=2\pi r^3$

$\pi r^3=64/2=32$

Now, the volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius. From above, we know that $\pi r^3=32$ , so we can plug this into the equation: